An X-ray stress measurement method and an X-ray stress measurement apparatus have been broadly known, and the applicant of this application has already proposed plural inventions (see JP-A-08-320264, JP-A-2000-213999, JP-A-2004-93404 and WO2012/015046A1). The conventional X-ray stress measurement apparatus generally has one X-ray source mounted therein, and it is configured to irradiate a sample as a measurement target with X-ray from the X-ray source, detect X-ray diffraction from the sample and non-destructively measure stress of the sample on the basis of information of the X-ray diffraction. A method called as “2θ-sin2 Ψ method” is known as such an X-ray stress measurement method as described above.
The 2θ-sin2 Ψ method will be briefly described hereunder.
In FIGS. 1A, 1B and 1C, a sample surface normal to a sample 1 is represented by N, and a lattice plane normal to internal crystal lattice planes of the sample 1 is represented by N′. The intersection angle Ψ between the sample surface normal N and the lattice plane normal N′ (generally called as “Ψ angle”) is varied from an angle state shown in FIG. 1A to an angle state shown in FIG. 1B and further varied to an angle state shown in FIG. 1C. At each Ψ angle, X-ray R0 is incident to the sample 1, X-ray diffraction R1 diffracted from the crystal lattice planes is detected by an X-ray detector (not shown) and a diffraction angle 2θ of each X-ray diffraction is determined.
Subsequently, the angle Ψ used for the measurement is converted to “sin2 Ψ”, and the value of sin2 Ψ and the value of 2θ measured every Ψ angle are plotted on a graph, and these plotted points are subjected to straight-line approximation to obtain a “2θ-sin2 Ψ line” as shown in FIG. 2. With respect to this 2θ-sin2 Ψ line, the gradient of the line is calculated by using the least-square method, and the calculated gradient is multiplied by a x-ray stress constant K, whereby a stress value as a measurement target is determined. The x-ray stress constant K is determined on the basis of the material properties (diffraction angle 2θ, Young's modulus and Poisson's ratio) of the sample and the wavelength of the X-ray used for the measurement.
In FIG. 2, a line A represents a state under which compression stress acts on the sample, and d1>d2>d3>d4 is satisfied. In FIG. 2, d1 to d4 represent lattice spacing. A line B represents a state under which free-stress acts on the sample, and d1=d2=d3=d4 is satisfied. A line C represents a state under which tensile stress acts on the sample, and d1<d2<d3<d4 is satisfied.
The 2θ-sin2 Ψ method described above has an advantage that the surface stress of the sample can be determined nondestructively with high accuracy. However, in order to determine the gradient according to the 2θ-sin2 Ψ method, it is required to vary the Ψ angle at least two times and measure the position value of the diffraction angle 2θ every time the Ψ angle is varied, so that this method requires a long measurement time.
Furthermore, in order to determine the stress gradient in a depth direction of the sample by using the X-ray stress measurement apparatus having one X-ray source as described above, it is required to vary the incident angle of the X-ray to the sample or repetitively perform the stress measurement while plural kinds of X-ray sources having different wavelengths are exchanged by one another. Therefore, this method has a problem that the measurement time is further longer.